It’s worth following up, to see if a) you’re still on the list and b) how long it might be. If you’re on the list, then because you were first on it while under-16 and in school, the NHS should cover the cost of your treatment and that might also be the reason it’s take. So long. There’s a shortage of dentists that offer nhs services, and the nhs can take forever before they pay for you to get them hence the long wait sometimes.
You can go privately , but it’s can be really expensive initially and the ongoing maintenance. If it’s causing and pain, then get in touch with your dentist.
Otherwise, it’s mainly cosmetic. Having nice teeth (straight and white essentially) is something most of us want, and were all self conscious about our smile and how we look. Just need to be confident with your appearance and who you are, and that should help overcome some of those feelings you have. (Until you get your braces at least)